The Sea Wharf Restaurant would like to determine the best way to allocate a monthly advertising budget of $$7,000\mathrm{.}00$ between newspaper advertising and radio

advertising. Management decided that at least $25\%$ of the budget must be spent on each type of media and that the amount of money spent on local newspaper

advertising must be at least twice the amount spent on radio advertising. A marketing consultant developed an index that measures audience exposure per dollar of

advertising on a scale from $0$ to $100,$ with higher values implying greater audience exposure. If the value of the index for local newspaper advertising is $40$ and the value of the index for spot radio advertising is $90,$ how should the restaurant allocate its advertising budget to maximize the value of total audience exposure?

$($a$)$ Formulate a linear programming model that can be used to determine how the restaurant should allocate its advertising budget in order to maximize the value of

total audience exposure. $($Assume $N$ is the amount spent on newspaper advertising and $R$ is the amount spent on radio advertising.$)$

Max

s$.$t$.$

budget

minimum newspaper spending

minimum radio spending

comparison radio and newspaper spending

$N,R0$

$($b$)$ Develop a spreadsheet model and solve the problem using Excel Solver. $($Round the Newspaper Dollars Allocated and the Radio Dollars Allocated to the nearest cent.

Round the Total Exposure Index to the nearest integer.$)$

Newspaper Dollars Allocated $

Radio Dollars Allocated $

Total Exposure Index